JP2000242774A - Image processing method and image processor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make improvable the degradation of the picture quality observed and a blur of a sharp edge by selecting an interpolation kernel corresponding to an edge strength index, an edge direction index and an edge context index concerning the discrete sample of a first set. SOLUTION: Image data are accessed, the text area of high contrast is detected and the edge strength and edge arrangement of image data are measured (S100-S110). The detected text domain and edge domain are coupled to a kernel or kernel parameter and a selection map concerning respective input pixels and cleaning is performed (S120 and S125). The edge domain is arranged on a uniformly directed edge domain or smooth background (S130). The cleaned kernel selection map is interpolated by using an NN interpolation kernel, and the kernel selection map or kernel parameter selection map is generated concerning respective output pixels (S135 and S140).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the field of resolution conversion of multidimensional digital data such as digital image data.

[0002]

2. Description of the Related Art Several methods are available for converting the resolution of digital data. A popular method is
It is a transform domain method such as a partial Fourier transform (partial FFT or Chirp-Z transform), a discrete cosine transform (DCT), and a discrete wavelet transform (DWT). In addition, many spatial domain methods such as resampling and digital filtering using finite impulse response filters (FIR) and infinite impulse response filters (IIR), usually continuous interpolation using cubic splines, etc. spatial domain method). When a continuous kernel produces data that passes through the original data points, the kernel is often called an interpolation kernel. If the generated interpolated data is not constrained to pass through the original data points, the kernel is often called an approximate kernel. The design of these continuous kernels has many constraints that must be met.

[0003] The continuous kernels commonly used for interpolation are the nearest neighbor (NN) kernel, the linear kernel, the quadratic kernel, and the cubic kernel. The NN kernel is the simplest method of interpolation, and interpolates an image with pixel values that are spatially closest to the image that requires interpolation. This method works very well when the scaling ratio is an integer multiple of the original data, because it preserves sharp edges without introducing new values (ie, without introducing new colors). However, non-integer ratios have the disadvantage of edge position shifting, which often produces visible distortions in the output image, especially in images containing text and fine line details.
On the other hand, linear interpolation allows the introduction of new gray levels (or colors) that are used effectively to locate edges at sub-pixel locations. This has the advantage of mitigating the effect of shifting edge positions, but sharp edges can appear blurry. Two-dimensional interpolation (quadr
atic interpolation) and cubic interpolation
Provides a steeper step response and therefore less blur at the edge, but a steeper response results in overshoot on either side of the edge.
These overshoots can make the edges of natural images look sharper, but on text, fine lines, and other computer-generated graphics, these overshoots are clearly visible and perceived image quality And impairs the readability of the text.

From the above, it can be concluded that each kernel has its own strengths and weaknesses. In addition, there are certain types of image regions that can best be interpolated using differently shaped kernels. Applying a single continuous convolution kernel to each image pixel does not meet all requirements for general-purpose resolution conversion applications.

One well-known method of generating a kernel with a steep step response but no overshoot is to adjust the parameters of the third order kernel according to the image information so as to eliminate the overshoot in the step response. is there. The two-parameter Catmull-Rom cubic equation has a kernel of the form:

(Equation 5)

[0006] The choices of parameters b and c that are frequently used are (b = 0, c = 0.5) and (b = 1, c = 0). The former is an interpolated cubic equation corresponding to the first three terms of the Taylor series expansion of the original image, and the latter is an approximate cubic B-spline. One well-known method is to fix the parameter b to b = 0 and c to be Gaussian Laplacian.
an of Gaussian: LOG) Vary between 0, 0.5 and 1 depending on the edge strength measured using an edge detector. For a sharp edge c = 0, the resulting cubic equation is:

(Equation 6)

[0007]

However, if the displacement of the resampled pixel is not very different from the displacement of the original pixel, for example when the resampling ratio is 10/11 or 11/10, this kernel is used. There is a problem with interpolating image data. In this example, pixels at the edges of text and other thin lines take on gray values instead of the original black or white values. This again results in sharp edges blurred and reduced image quality observed.

A further problem with conventional continuous convolution kernels arises when applying this to edges that are in the diagonal direction of the image plane. Existing kernels can be applied in a separable way, ie first applied to the rows of the image and then applied to the columns, or in a two-dimensional form where the kernel is directly convolved with the two-dimensional image data You can also. However, the orientation of the kernel in these implementations is limited to either horizontal, vertical, or symmetric. When a diagonal edge is encountered, pixels on either side of the edge, rather than along the edge, are used primarily for interpolation. This results in the interpolated edges no longer appearing vivid and smooth, but appear to be jagged, blurred, or both. A solution to the above problem is known to prevent interpolation in the direction across the edge by using pixel value estimates for pixels on the other side of the edge in bilinear interpolation. . However, this method requires very accurate sub-pixel edge estimates at the output resolution and iterative post-processing using a continuous approximation procedure. Both of the above methods require a lot of memory and processing resources. Another approach to this problem is to utilize a set of two-dimensional "steerable" kernels that can be directed along the edge line during image interpolation. In this method, smoothing is performed along the edge line (jagging of the edge is reduced), but smoothing is not performed in a direction crossing the edge (the sharpness of the edge is maintained).

[0009] Methods for selecting an interpolation kernel based on edge strength or user input are known. However, there are some drawbacks that prevent this method from working optimally. First, using only edge strength as the basis for kernel selection does not provide enough information for reliable kernel selection (especially at diagonal edges). Second, kernel selection based solely on user input is impractical and does not specify a sufficiently detailed kernel selection. For example, in the sub-image shown in FIG. 7A, there is no ideal kernel for the entire sub-image.
Generally, different kernels are required at resolutions that cannot be specified by the user.

It is an object of the present invention to remedy one or more of the disadvantages of the prior art.

[0011]

According to the present invention, one of a plurality of interpolation kernels is used to interpolate a first set of discrete sample values to produce a second set of discrete sample values. The method, wherein the interpolation kernel comprises:
For a set of discrete sample values, the edge strength index,
A method is provided, wherein the method is selected according to an edge direction indicator and an edge context indicator.

According to a further aspect of the invention, there is provided a method of interpolating a first set of discrete sample values using a single interpolation kernel to generate a second set of discrete sample values, the method comprising: A method is provided, wherein a kernel is selected for the first set of discrete sample values in response to an edge strength indicator, an edge direction indicator, and an edge context indicator.

According to a further aspect of the invention, there is provided a method of image data interpolation, the method comprising: accessing a first set of discrete sample values of the image data; Edge placement index,
Calculating a kernel value of each of the discrete sample values using one of a plurality of kernels according to an edge strength indicator and an edge context indicator; convolving the discrete sample value with the kernel value; Second
A method comprising providing a set of

According to a further aspect of the invention, there is provided an apparatus for interpolating image data, the apparatus comprising: means for accessing a first set of discrete sample values of the image data; Calculator means for calculating a kernel value of each of the discrete sample values using one of a plurality of kernels according to an edge arrangement index, an edge strength index, and an edge context index for the discrete sample values; Convolve the discrete sample value with the value,
An apparatus is provided that includes convolution means for providing a second set of discrete sample values.

According to a further aspect of the invention, there is provided a computer readable medium for processing data, the program storing a program for an apparatus including an image data interpolation method, wherein the program comprises Code for accessing a first set of discrete sample values of the data, and for each of the discrete sample values, using one of a plurality of kernels according to an edge location indicator, an edge strength indicator, an edge context indicator. A program is provided that includes code for calculating a kernel value for each discrete sample value, and code for convolving the kernel value with the discrete sample value and providing a second set of discrete sample values. Is done.

According to a further aspect of the present invention, there is provided a method for interpolating image data comprising a first mapping of discrete sample values, the method comprising: (i) identifying a text region in the first mapping. Labeling each discrete sample value within each text region; and (ii) calculating edge information for each discrete sample value of the image data to identify an edge sample value; Saving the placement angle for
(Iii) combining the label and the placement angle for each of the discrete sample values to form a second mapping of the discrete sample values; and (iv) for each edge sample value within the second mapping. Manipulating the placement angle to form a third mapping of the discrete sample values; and (v) manipulating the image data of the third mapping to form a fourth mapping of the image data. And (vi) interpolating each sample value of the fourth mapping with a first kernel among a plurality of kernels according to the label and the arrangement angle of each sample value of the fourth mapping, A method is provided that includes forming a fifth mapping of the image data.

According to a further aspect of the present invention, there is provided an apparatus for interpolating image data including a first mapping of discrete sample values, the apparatus identifying a text region in the first mapping, Means for labeling each discrete sample value in each text region; identifying edge sample values by calculating edge information for each discrete sample value of the image data; storing an arrangement angle for each edge sample value First calculating means for combining the label and the placement angle for each of the discrete sample values to form a second mapping of the discrete sample values; and Manipulating the placement angle for each edge sample to form a third mapping of the discrete sample values; Operating means for manipulating the image data to form a fourth mapping of the image data; and each sample of the fourth mapping according to the label and the arrangement angle of each sample value of the fourth mapping. An apparatus is provided that includes interpolating means for interpolating a value with a first kernel of a plurality of kernels to form a fifth mapping of the image data.

According to a further aspect of the invention, there is provided a computer readable medium for storing a program for an apparatus for processing data, wherein the processing comprises the step of transferring image data comprising a first mapping of discrete sample values. A code for identifying a text region in the first mapping and labeling each discrete sample value in each text region, the program comprising: Calculate edge information to identify edge sample values, code for storing an arrangement angle for each edge sample value, and combine the label and the arrangement angle for each discrete sample value; Code for forming a second mapping, and for each edge sample in the second mapping Code for operating the serial arrangement angle to form a third mapping of the discrete sample values,
A code for manipulating the image data of the third mapping to form a fourth mapping of the image data, and the label of each of the sample values of the fourth mapping and the arrangement angle. A medium is provided that includes code for interpolating each sample value of a fourth mapping with a first kernel of a plurality of kernels to form a fifth mapping of the image data.

[0019]

DESCRIPTION OF THE PREFERRED EMBODIMENTS When resampling a digital image, smooth areas and edge areas need to be resampled in different ways. Parameter c = 0.5
Long symmetric kernels such as conventional Catmull-Rom cubic equations with are ideal for smooth image regions.
Short kernels, such as Catmull-Rom cubic equations with parameter c = 0, are generally suitable for edges and corners, and highly textured regions. However, in order to reduce the jagged impression of the oblique edge, the edge direction must be taken into account in the interpolation process. The direction of the edge is also important so that interpolation can be smooth along the edge, not across the edge. In this way, the contour of the edge is kept smooth, while the change of the edge is kept sharp.

The first embodiment of the present invention discloses an image interpolation method for automatically selecting an appropriate interpolation kernel for each image area. This selection is based not only on edge strength information, but also on edge direction information and local edge context information. In addition, high contrast text regions are detected and interpolated to preserve the shape and contrast of the text.

In a second embodiment of the present invention, the parameters of a single interpolation kernel are adjusted so that the kernel is reshaped appropriately for each region in the image.

The proposed resolution conversion method first identifies high-contrast text regions and measures both edge strength and edge direction of the image data. In the first embodiment, text information and edge information are then used to select an appropriate interpolation kernel to use. In a second embodiment, the parameters of the interpolation kernel are adjusted using edge strength and edge orientation data.
Thereafter, unnecessary kernel changes are removed using text and contextual information from the edge map to prevent inappropriate kernel selection. This post-processing on raw edge information is necessary to reduce and eliminate artifacts due to interpolation.

The disclosed interpolation method according to the preferred embodiment will be briefly described with reference to FIG. The method comprises a series of steps described in more detail later in this specification. The process begins at step 100, where image data is accessed. The process continues at step 105, where high contrast text regions are detected. In step 110, the edge strength and the edge arrangement of the image data are measured. The detected text regions include cases of isolated pixels or pixel groups that are classified as text. To reduce the possibility of unnecessary interpolation kernel switching,
These cases need to be removed. Which in the preferred embodiment, the binary text map known form _opening operation in the conventional image processing for (morphological
It is performed in the next step 115 using an _opening operation. The process continues to the next step 120, where the detected text and edge regions are combined into a kernel, or kernel parameter, selection map for each input pixel. In the next step 125, the kernel selection map or kernel parameter selection map is cleaned. This involves rearranging the edge regions with a uniformly oriented edge region or a smooth background down to produce a kernel selection map that has been cleaned in step 130. The cleaned kernel selection map is at the input pixel resolution. The process continues to the next step 135 where the cleaned kernel selection map is N
Interpolated using an N interpolation kernel. The result of the NN interpolation is to generate a kernel selection map, or kernel parameter selection map, for each output pixel at step 140. In the next step 145, an appropriate interpolation kernel is applied to the image data based on the output resolution kernel selection map. The interpolation kernel applied to the image data at step 145 may be, according to a preferred embodiment, a generic cubic kernel 150, which is disclosed later in this specification. The process ends at step 155, where the resolution converted output image is preferably displayed or further processed, such as by a graphics processor.

The above steps need not operate on the entire image at one time. However, for simplicity, the preferred embodiment describes the processing of the entire image of input pixels. It is imperative that the algorithm according to the preferred embodiment operate in a memory-located manner, such that only a limited number of rows of the input image (preferably 5 rows in the raster scan direction) are required at a time. Not desirable though. As an alternative, the algorithm can be applied to any image sub-region or block.

The following description of the preferred embodiment will refer to red,
This document describes a color image expressed in a green, blue (RGB) color space. With appropriate changes, this technique can be easily applied to gray level images (only one color plane) or any color space representation (YUV, YCbCr, etc.). Alternatively, if the images are provided in another color space, they can be converted to the RGB color space before processing.

The above steps of the present invention will be described in more detail with reference to FIGS.

[0027] Text Detection and Text Map Creeping
Figure the cleaning of detection and text map of the training step text 2
Will be described. Local contrast between adjacent pixels is used as a basis for text region detection. Text regions are typically regions with high local contrast, a limited number of colors, and a simple texture. The use of these criteria also allows for the detection of multilingual text information expressed in high contrast.

The process begins at step 200, where the text map is initialized to be smooth. In the next step 205, the following step 215
Through 230 are performed for each color plane and each pixel in the image. Each pixel and color plane of the input image is scanned with a 3 × 3 neighborhood operator. In step 215, the value C
Are compared to a threshold value Ttxt, where C is given by: C = max (| P ₀ −P _i |), i∈1,. . , 8 (3) where i is the index of the eight neighboring pixels closest to the center pixel P0. In the preferred embodiment, a value of Ttxt = 220 is used. In the next step 220, the value of C is compared with a threshold value Ttxt.
When the value of C exceeds the threshold Ttxt, the pixel P0
Are labeled in step 225 as text areas.

The detected text regions include the case of isolated pixels or groups of pixels, labeled as text. These cases need to be eliminated to reduce the chance of unnecessary interpolation kernel switching. This is performed in a preferred embodiment in the next step 230 using a form opening operation known in conventional image processing for binary text maps. The structuring element defined by the matrix S is used to clean the text detection map as follows.

(Equation 7)

The form release operation is defined as erosion with S followed by dilation and removes the following pattern (including this rotated mold):

(Equation 8)

The process of detecting text and cleaning the text map is completed after steps 215 through 230 have been performed for each pixel in the image.

Edge strength and direction detection step The edge strength and direction detection step will be described with reference to FIG. The process begins at step 300, where Ed
GeMap is initialized smoothly. Next step 3
At 05, the following steps 315 to 335 are performed for each color plane and each pixel in the image. In step 315, horizontal and vertical edge responses, referred to as Gh and Gv, respectively, are calculated for each input image pixel. In the preferred embodiment, this is performed using a 5-tap optimal edge detector as is known in the art. The coefficients used to form Gh and Gv are shown in Table 1.

[Table 1] Table 1 shows the edge detection coefficients used in the preferred embodiment. Shown are a low-pass (interpolated) kernel and a high-pass (first derivative) kernel.

In the next step 320, a gradient magnitude Gm is obtained from the intensities of these two components using the following equation: G _m = √ (G _v ² + G _h ² ) (5)

The maximum gradient values of the R, G, and B components are used to determine the overall edge gradient strength. The process continues to the next step 320, where the gradient magnitude Gm is compared to a threshold Gth. If this is less than the threshold, the pixel is classified as a non-edge pixel. If not, at step 330, the pixel is classified as an edge pixel and the edge direction Gθ is recorded in EdgeMap.
Therefore, the color plane with the highest gradient strength is used to estimate the edge direction for each input pixel.
The edge gradient direction Gθ is estimated using the following equation. _{^{Gθ = tan -1 (G v /}} G h) (4)

The process continues at step 335, where the edge pixel directions are horizontal (0), vertical (π / 2),
It is quantized to one of four cases of diagonal (π / 4) and anti-diagonal (3π / 4).

The process of detecting the edge strength and the edge direction comprises the steps 315 to 3 for each pixel in the image.
Complete after 35 has been performed.

It should be noted that increasing the number of quantization bins and interpolating with correspondingly located steerable kernels produces better interpolated output. However, this increases the complexity of the implementation, so quantization in four directions is used in the preferred embodiment.

Kernel selection of text information and edge information
Next, the combination of text information and edge information into a kernel selection map will be described with reference to FIG.
The input image is assumed to be smooth except for pixels where edge regions or text regions are detected. Therefore, the kernel selection map is initialized at step 400 to select a general smoothing kernel. In the preferred embodiment, a cubic interpolation kernel with a parameter c = 0.5 is used to interpolate pixels within these smooth regions. The process continues to step 405, where steps 410 through 425 are performed on the pixels in the input image, where text region information and edge region (edge direction) information are overlaid on the kernel selection map. If there is both a text area and an edge area, the text area information has priority. There are many edge activities in the text area, and considering them as directional edges causes excessive kernel switching, and therefore visual artifacts (artefac
It is important that text regions take precedence over edge regions because they can result in ts). Process 4
Continuing to 10, where a check is performed to see if the current pixel in the EdgeMap is classified as smooth. If the current pixel in EdgeMap is not smooth, EdgeMap information is recorded in KernelMap in step 415. In the next step 420, a check is performed to see if the current pixel in the TextMap is classified as smooth. TextMa
Text if the current pixel in p is not smooth
The Map information is set to KernelMa
Recorded in p. Combining the text and edge information into the kernel selection map process is complete after steps 410 through 425 have been performed for each pixel in the image.

Cleaning the Kernel Selection Map The cleaning of the kernel selection map process is described with reference to FIG. Isolated edge directions may occur in local areas where other points are uniformly oriented. It is best for these sparsely distributed edge regions to be rearranged with uniformly arranged edge regions or a smooth background. This also prevents excessive kernel switching that can cause visual artifacts in the interpolated image.

The process begins at step 500, where the accumulator is initialized. In the next step 505, steps 510 to 540 are executed for each 5 in the
Executed for × 5 blocks. In step 510, the number of edge pixels (including text and background) of each edge arrangement is accumulated in the vicinity of 5 × 5. The process continues to step 515, where a number of edge locations are identified. In a next step 520, a small number of edge configurations are identified. A large number of edge arrangements and a small number of edge arrangements are identified, and a small number of edge pixels are reassigned to a large number of arrangements in the next step, with the exception of pixels identified as text regions. Next Step 5
At 25, the calculated multiple edge placements are Tmajor
And the calculated small number of edge locations is Tmino
r. In step 530, if there are more pixels than Tmajor in the 5 × 5 area, the arrangement is set to many arrangements, and if there are fewer pixels than Tminor in the 5 × 5 area, the arrangement is set to few arrangements. Is done. In a preferred embodiment, the multiple threshold Tmajor
Is 15, and the minority threshold Tminor is 5. 5x
The total number of pixels in the five regions is 25. If the accumulated edge pixels are greater than the multiple threshold, multiple edge directions are assigned. If the accumulated edge pixels are not more than the majority threshold, the pixel area is not changed.
A large number or a small number of arrangements may be a background or a text area. Next step 53
At 5, the 5x5 pixel block moves one column along the image buffer and the process repeats for the next adjacent 5x5 pixel block. These blocks do not overlap each other in any single pass of the image. The process repeats a fixed number of times, step 5 to see if 5 iterations have been completed at the point where the process is completed.
At 40, a check is performed. In a preferred embodiment,
Five repetitions are sufficient to clean the map to a reasonable extent, but five repetitions are not required.

Kernel selection map with interpolation cleaned
The steps of applying interpolation to the cleaned kernel selection map applied to are described with reference to FIG. The process begins at step 600 where the kernel selection map (K
ernMap) is interpolated to the same size as the output image. Neighbor (NN) interpolation is used to obtain a kernel selection map at the required output resolution. NN interpolation is used to reduce the computational costs associated with more complex interpolation methods (linear, cubic, etc.) without significantly reducing the output image quality. Instead, the NN interpolation is not actually performed, and the kernel is selected in the O / P image according to the closest pixel in the KernelMap.

The kernel selection map (KernelMa)
After p) is interpolated to the same size as the output image, each input is read so that the correct interpolation kernel can be used.
In the next step 610, a check is performed to see if the KernelMap information is classified as text. If KernelMap = text, then in step 615 the text pixel was modified 3
Interpolated by the next kernel. The modified cubic kernel h (s) of the preferred embodiment is given by:

(Equation 9) In the above equation, s = t / Δt is a normalized coordinate having an integer value at the sample point.

In the preferred embodiment, parameter d is set to 0.2. Note that this kernel has a reduced size of 2x2.

If the KernelMap has not been classified as text, the process continues to step 620 where a check is performed to see if the KernelMap information has been classified as an edge. If KernelMap = Edge, then in step 625 the edge pixels are interpolated with one of the four steerable cubic kernels. As h (s _x , s _y ), the steerable kernel of the preferred embodiment is given by:

(Equation 10) In the above equation, sx = x / Δx and sy = y / Δy are resampling distances in the horizontal and vertical directions, respectively.
Indicates matrix multiplication. The quantized edge constellation defines the required constellation of steerable cubic kernels, either 0, π / 4, π / 2, or 3π / 4.

The process continues at step 630, where if the KernelMap is not classified as an edge, a check is performed to see if the KernelMap information is smooth. KernelMap =
In the smooth case, the pixel is a conventional Catmull-R
Interpolated by an om3 order kernel (b = 0, c = 0.5).

FIGS. 7-9 illustrate the interpolation effectiveness of the present invention on many typical images. FIG. 7A shows an original image at a certain resolution before interpolation is performed. FIG. 7 (b) shows the image of FIG. 7 (a) at a higher resolution after interpolation using a conventional cubic kernel. In contrast, FIG. 7 (c) shows the image of FIG. 7 (a) at a higher resolution after interpolation according to the preferred embodiment of the present invention. It can be seen that FIG. 7 (c) shows an image with sharper edges and less blur than FIG. 7 (b).

FIG. 8 (b) shows the text image of FIG. 8 (a) enlarged 2.7 times in both directions using the interpolation method according to the preferred embodiment of the present invention.

FIG. 9A shows a graphic image interpolated using a conventional NN kernel. FIG. 9 (b) shows the same graphic image interpolated using the interpolation method according to the preferred embodiment of the present invention. From the image of FIG. 9B, it can be seen that the oblique line is smoother along that direction than in FIG. 9A.

According to the second embodiment of the present invention, Kern
The elMap does not include encoding for different kernels that can be used for interpolation, but includes parameter values that apply to one "generic" kernel. Conventional kernel of equation (1), modified kernel of equation (5), fully steerable 3 of equations (6), (7), (8), (9)
The definition of the general-purpose cubic interpolation kernel , which is a combination of the next kernels , is as follows.

[Equation 11]

Here, the intersection edge weighting coefficient (the acr
oss edge weighting factor) w (θ) is θ = 0, π /
This is a smooth function limited to pass 1 when s and π and pass √2 when θ = π / 4 and 3π / 4. The functions used in the preferred embodiment are as follows:

(Equation 12) Then, the general-purpose interpolation kernel h (s) is given by the following equation.

(Equation 13) In the above equation, d is a parameter that controls the width of the “dead zone” of the cubic interpolation kernel.

Based on the kernel parameter map, the input image area is interpolated with a general cubic kernel with parameters set as follows:

The text area has an edge arrangement angle parameter θ = 0, a “dead zone” parameter d = 0.2,
It is interpolated using the following equation parameters b = 0 and c = 0. This gives a reduced 2 × 2 size kernel, ie the remaining kernel coefficients are all zero.

The edge region has θ set to one of 0, π / 4, π / 2, or 3π / 4 (depending on the edge angle Gθ), d = 0, b = 0, c = 0. .5. Six or eight of these coefficients will be zero depending on the placement angle (θ), which is a 4 × 4 kernel.

In the smooth region, θ = 0, d = 0, b =
Interpolated using 0, c = 0.5. This is a 4x4 non-zero kernel.

Preferred Embodiment of the Apparatus The preferred method is preferably implemented using a conventional general purpose computer system, such as the system 1000 shown in FIG. 10, in which the processes of FIGS. Can be implemented as software running on a computer. In particular, the steps of the method are performed by instructions in software executed by a computer. The software can be split into two parts, one part performing the method of the preferred embodiment and another part managing the user interface between the latter and the user. This software can be stored in a computer-readable medium including a storage device described later, for example. The software is loaded onto the computer from a computer readable medium and then executed by the computer. A computer readable medium having such software or a computer program recorded thereon is a computer program product. The use of a computer program product in a computer preferably implements an advantageous device for directing character strokes or n-dimensional finite space curves according to embodiments of the present invention.

The computer system 1000 has a computer module 1002, a video display 1016, and input devices 1018 and 1020. Further, the computer system 1000 includes a computer module 1002
It is possible to have any number of other output devices, including line printers, laser printers, plotters, and other playback devices connected to the device. Computer system 1000 can connect to one or more other computers via communication interface 1008c using a suitable communication channel 1030, such as a modem communication path, a computer network, or the like. The computer network is a local area network (LA)
N), wide area network (WAN), intranet,
And / or the Internet.

The computer module 1002 is a central processing unit (a plurality of units) (hereinafter simply referred to as a processor).
1004, a memory 10 that can include a random access memory (RAM) and a read only memory (ROM)
06, an input / output (IO) interface 1008, a video interface 1010, and one or more storage devices generally represented by block 1012 in FIG. Storage device (s) 1012 may include one or more of a floppy disk, hard disk drive, magneto-optical disk drive, CD-ROM, magnetic tape, or many other non-volatile storage devices known to those skilled in the art. Can be included. Components 1004 to 10
Each of the 12 typically 1 via a bus 1014
Connected to one or more other devices, bus 1014 comprises:
It has data, address, and control buses.

Video interface 1010 is connected to video display 1016 and provides video signals from computer 1002 for display on video display 1016. User inputs operating the computer 1002 include:
It can be provided by one or more input devices 1008. For example, an operator can provide input to computer 1002 using a keyboard 1018 and / or a pointing device such as a mouse 1020.

[0059] Computer system 1000 is provided for purposes of illustration only, and other configurations may be employed without departing from the scope and spirit of the invention. An example of a computer that can execute the present embodiment is an IBM-PC / AT or compatible machine, one PC of the Macintosh (TM) series, Sun Spa
rcstation (TM) or a configuration developed from these. The foregoing computers are merely examples of the types of computers on which embodiments of the present invention may be implemented. Typically, the processes of the embodiments described below involve software recorded on a hard disk drive (typically depicted as block 1012 in FIG. 10) as a computer-readable medium. And a resident program.
4 to be read and controlled. Programs, pixel data,
Intermediate storage of any data is achieved using the semiconductor memory 1006 and may cooperate with the hard disk drive 1012.

In some examples, the program is a CD-R
It is encoded on an OM or floppy disk (both generally depicted by block 1012) and supplied to the user, or alternatively is read by the user from a network, for example, via a modem device connected to a computer. In addition, software may be stored on magnetic tape, ROM or integrated circuits, magneto-optical disks, wireless or infrared transmission channels between computers and other devices, computer readable cards such as PCMCIA cards, e-mail transmissions and websites The information can be loaded into the computer system 1000 from another computer-readable medium, including the Internet and an intranet, containing the information. The aforementioned medium is
It is merely an example of the relevant computer-readable media. Other computer readable media can be executed without departing from the scope and spirit of the invention.

The preferred method of reconstructing a continuous signal can alternatively be implemented in dedicated hardware, such as one or more integrated circuits that perform the functions or sub-functions of the method steps. Such dedicated hardware may include a graphics processor, a digital signal processor, or memory associated with one or more microprocessors.

While the foregoing describes only two embodiments of the present invention, those skilled in the art will be able to modify and / or modify the same without departing from the scope and spirit of the present invention. It is possible to change.

As described above, according to the present invention,
It is possible to classify an image into regions according to its features, and perform image interpolation by selecting the optimal interpolation kernel for each of the classified regions using sufficient information to select a reliable kernel. it can. Therefore, it is not necessary to select a kernel based on a user's input, and an image can be interpolated by selecting an optimal kernel even in an area that cannot be specified by the user.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a method of interpolation according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating a text detection method according to the interpolation method of FIG. 1;

FIG. 3 is a flowchart illustrating a method of detecting edge intensity and arrangement by the interpolation method of FIG. 1;

FIG. 4 is a flowchart illustrating a method of combining a text map and an edge map according to the interpolation method of FIG. 1;

FIG. 5 is a flowchart illustrating a method of cleaning a kernel selection map by the interpolation method of FIG. 1;

FIG. 6 is a flowchart illustrating a method of interpolating an output image by the interpolation method of FIG. 1;

FIG. 7A illustrates an original image having a predetermined resolution. FIG. 7 (b) shows the image of FIG. 7a at a higher resolution after interpolation using a conventional cubic kernel. FIG. 7c shows the image of FIG. 7a at a higher resolution after interpolation according to the first embodiment of the invention.

FIG. 8A is a diagram showing an original text image. (B) FIG. 8 after interpolation by the embodiment of the present invention
It is a figure showing the text image of (a).

FIG. 9A illustrates a graphic image interpolated using a conventional NN kernel. FIG. 9B shows the graphic image of FIG. 9A after being interpolated according to the first embodiment of the present invention.

FIG. 10 is a configuration diagram of a general-purpose computer that can execute the embodiment.

 ──────────────────────────────────────────────────の Continued on the front page (72) Inventor Kai Hong 2113 Thomas Holt Drive, North Ryde, New South Wales 1 Canon Information Systems Research Australia Proprietary Limited

Claims (108)

[Claims] 1. A method for interpolating a first set of discrete sample values using one of a plurality of interpolation kernels to generate a second set of discrete sample values, the method comprising: A method wherein a kernel is selected for each of the first set of discrete sample values in response to an edge strength indicator, an edge direction indicator, and an edge context indicator. 2. The method according to claim 1, wherein the interpolation kernel is a general-purpose interpolation kernel h.
The method of claim 1, wherein (s). 3. The general-purpose interpolation kernel h (s) is given by s =
Assuming that t / Δt and 0 ≦ d <0.5, 3. The method of claim 2 in the form: 4. The s _x = x / Δx and s _y = y / Δy are horizontal and vertical resampling distances, respectively.
Assuming that “·” indicates a matrix multiplication, the plurality of kernels are represented by The method of claim 1 provided by: 5. The method of claim 1, wherein the first set of discrete sample values comprises:
The method of claim 1, wherein the resolution is different than the second set of discrete sample values. 6. Interpolating a first set of discrete sample values using a single interpolation kernel, and interpolating a second set of discrete sample values.
Wherein the interpolation kernel is selected for the first set of discrete sample values according to an edge strength indicator, an edge direction indicator, and an edge context indicator. 7. The interpolation kernel according to claim 1, wherein the interpolation kernel is a general-purpose interpolation kernel h.
7. The method of claim 6, wherein (s). 8. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: The method of claim 7 in the form of: 9. The first set of discrete sample values comprises:
The method of claim 6, wherein the resolution is different than the second set of discrete sample values. 10. A method of image data interpolation, comprising: accessing a first set of discrete sample values of the image data; and for each of the discrete sample values, an edge placement indicator, an edge intensity indicator, and an edge context indicator. Computing a kernel value for each of the discrete sample values using one of a plurality of kernels in response to: convolving the kernel value with the discrete sample value to provide a second set of discrete sample values. And a method comprising: 11. The kernel according to claim 1, wherein the kernel is a general-purpose interpolation kernel h.
The method of claim 10, wherein (s). 12. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: The method of claim 11 in the form: 13. Assuming that s _x = x / Δx and s _y = y / Δy are horizontal and vertical resampling distances, respectively, and that “·” indicates a matrix multiplication, the plurality of kernels are: Equation 2 A method according to claim 11, wherein the method is provided by: 14. The method of claim 10, wherein the first set of discrete sample values has a different resolution than the second set of discrete sample values. 15. An apparatus for interpolating image data, comprising: means for accessing a first set of discrete sample values of the image data; and for each of the discrete sample values, an edge placement indicator, an edge intensity indicator, Calculator means for calculating a kernel value of each discrete sample value using one of a plurality of kernels according to an edge context index; convolving the discrete sample value with the kernel value; Convolving means for providing a second set. 16. The apparatus according to claim 15, wherein said interpolation kernel is a universal interpolation kernel h (s). 17. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: 17. The device of claim 16, wherein the device is in the form: 18. The plurality of kernels, where s _x = x / Δx and s _y = y / Δy are horizontal and vertical resampling distances respectively, and “·” indicates a matrix multiplication, Equation 2 16. The device according to claim 15, provided by: 19. The apparatus of claim 15, wherein the first set of discrete sample values has a different resolution than the second set of discrete sample values. 20. A computer readable medium for processing data, the program storing a program for an apparatus including an image data interpolation method, the program comprising: discrete sampled values of the image data. Code for accessing a first set of discrete sample values for each of the discrete sample values using one of a plurality of kernels according to an edge placement indicator, an edge intensity indicator, and an edge context indicator. A computer-readable medium comprising: code for calculating a kernel value of; and code for convolving the kernel value with the discrete sample values and providing a second set of discrete sample values. 21. The computer readable medium according to claim 20, wherein said interpolation kernel is a universal interpolation kernel h (s). 22. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: 22. The computer readable medium of claim 21 in the form of: 23. Assuming that s _x = x / Δx and s _y = y / Δy are resampling distances in the horizontal and vertical directions, respectively, and that “·” indicates matrix multiplication, the kernel is expressed as ] 22. The computer readable medium of claim 21 provided by: 24. The computer readable medium of claim 20, wherein the first set of discrete sample values has a different resolution than the second set of discrete sample values. 25. A method for interpolating image data comprising a first mapping of discrete sample values, the method comprising: (i) identifying text regions in the first mapping; Labeling each discrete sample value; (ii) calculating edge information for each discrete sample value of the image data to identify an edge sample value, and storing an arrangement angle for each edge sample value. (Iii) combining the label and the placement angle for each of the discrete sample values to form a second mapping of the discrete sample values; and (iv) for each edge sample value within the second mapping. Manipulating the placement angle to form a third mapping of the discrete sample values; (v) the third mapping Manipulating the image data of the ping to form a fourth mapping of the image data; and (vi) responsive to the label and the placement angle of each sample value of the fourth mapping, the fourth mapping. Interpolating each sample value of said mapping with a first kernel of a plurality of kernels to form a fifth mapping of said image data. 26. Step (v) comprises: (v) (a) associating each discrete sample value of the fourth mapping with a corresponding discrete sample value of the third mapping; And b.) Scaling the third mapping of the image data based on the association. 27. The method of claim 25, wherein step (v) includes interpolating the image data of the third mapping using a second kernel. 28. The method according to claim 28, wherein the second kernel is NN (nearest n
27. The method of claim 26, which is an interpolation kernel. 29. The method of claim 1, wherein the label and the placement angle of each sample value of the fourth mapping are used to determine the first
Selecting a kernel parameter value for the kernel of the second step.
5. The method according to 5. 30. The method according to claim 25, wherein said first kernel is a generic interpolation kernel h (s). 31. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: 31. The method of claim 30, wherein the method is in the form: 32. A s _{x =} x / Δx and s _{y = y} / Δy is resampling distance in the horizontal and vertical directions, respectively, as "-" indicates a matrix multiplication, the plurality of kernels, [ Equation 2 26. The method of claim 25, provided by: 33. Steps (i) to (vi) include:
26. The method of claim 25, wherein the method is performed on one of a plurality of portions of the first mapping of discrete sample values of the image data. 34. The method of claim 25, wherein a label takes precedence over said placement angle when forming said second mapping of said discrete sample values. 35. The method of claim 25, wherein the fourth mapping has a different resolution than the first mapping. 36. The method according to claim 25, wherein said image data is color image data. 37. The method of claim 36, wherein steps (i) and (ii) are performed for each color plane of the color image data. 38. The method according to claim 36, wherein steps (i) and (ii) are performed on a luminance component of the color image data. 39. Step (i) comprises: (i) (a) calculating a text index value C; and (i) (b) comparing the text index value with a threshold value, and Wherein said labeling of discrete sample values comprises a sub-step based on said comparison. 40. The text index C is: C = max
(| P ₀ −P _i |), i∈1,. . , 8 and i
There The method of claim 39 which is closest eight neighboring discrete sample index to the central discrete sample values P ₀ (index). 41. The method of claim 39, wherein step (i) comprises: (i) (c) performing a cleaning operation on the text label. 42. The cleaning operation is a morphological opening operation.
2. The method according to 1. 43. Step (ii) comprises: (ii) (a) calculating an edge response value for each of the discrete sample values; and (ii) (b) calculating a gradient magnitude value based on the edge response value. (Ii) (c) comparing the gradient magnitude value to a threshold; (ii) (d) classifying a current pixel based on the comparison; (ii) (e). 26. The method of claim 25, comprising :)) calculating the placement angle for a current pixel based on the comparison; and (ii) (f) storing the placement angle. 44. The gradient magnitude value G _m , where G _v and G _h are a vertical edge response and a horizontal edge response, respectively, wherein G _m = エ ッ ジ (G _v ² + G _h ² ). the method of. 45. Assume that G _v and G _h are a vertical edge response and a horizontal edge response, respectively, and
The method of claim 43 which is _{^{Gθ = tan -1 (G v /}} G h). 46. Step (iv) comprises: (iv) (a) one of a plurality of portions of said discrete data value.
(Iv) (b) calculating the maximum and minimum values of the discrete sample values for each configuration angle; and (iv) (c) Iv) comparing the maximum value and the minimum value to a maximum threshold value and a minimum threshold value, respectively; and (iv) re-assigning an arrangement angle of the discrete data values of the portion based on the comparison. (Iv) (e) repeating steps (iv) (a) through (iv) (e) for each portion of the discrete data value. 47. The method of claim 46, wherein said plurality of portions of said discrete data values are five portions. 48. The method of claim 25, wherein the modified cubic interpolation kernel is applied to discrete data values labeled as text. 49. The modified cubic interpolation kernel h (s), where s = t / Δt is a normalized coordinate having an integer value at a sample point and 0 ≦ d <0.5.
Is: 49. The method of claim 48 in the form. 50. The method of claim 25, wherein a steerable cubic interpolation kernel is applied to discrete data values classified as edges. 51. Assuming that s _x = x / Δx and s _y = y / Δy are resampling distances in the horizontal and vertical directions, respectively, and that “·” indicates matrix multiplication, The interpolation kernel is 51. The method of claim 50 in the form: 52. The method of claim 50, wherein a conventional cubic interpolation kernel is applied to discrete data values classified as smooth. 53. Assuming that b = 0 and c = 0.5, the conventional cubic interpolation kernel is given by: 53. The method of claim 52 in the form: 54. An apparatus for interpolating image data including a first mapping of discrete sample values, comprising identifying text regions in the first mapping and applying each discrete sample value in each text region. Means for labeling; first calculating means for calculating edge information for each of the discrete sample values of the image data to identify edge sample values, and storing an arrangement angle for each of the edge sample values; Combining means for combining the label and the placement angle for each discrete sample value to form a second mapping of the discrete sample values; and operating the placement angle for each edge sample in the second mapping. Forming a third mapping of the discrete sample values and manipulating the image data of the third mapping to generate a third mapping of the image data. Operating means for forming four mappings; and, according to the label and the arrangement angle of each of the sample values of the fourth mapping, each of the sample values of the fourth mapping is a first of a plurality of kernels. Interpolating means for interpolating with a kernel to form a fifth mapping of the image data. 55. The apparatus according to claim 55, further comprising: converting each discrete sample value of the fourth mapping to the third
55. The apparatus of claim 54, further comprising: associating means for associating a corresponding one of the mappings with corresponding discrete sample values; and scaling means for scaling the third mapping of the image data based on the associating. 56. The apparatus of claim 54, further comprising interpolating means for interpolating said image data of said third mapping using a second kernel. 57. The apparatus according to claim 56, wherein said second kernel is an NN interpolation kernel. 58. Using the label and the placement angle of each of the sample values of the fourth mapping to determine the first
6. Selecting a kernel parameter value for the kernel of claim 5.
An apparatus according to claim 4. 59. The apparatus according to claim 54, wherein said first kernel is a generic interpolation kernel h (s). 60. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: 60. The device of claim 59 in the form: 61. a resampling distance s _{x =} x / Δx and s _{y = y} / Δy are the horizontal and vertical directions, respectively, as "-" indicates a matrix multiplication, a plurality of kernels above, (Equation 2) 56. The device of claim 54, provided by: 62. The apparatus of claim 54, wherein a label takes precedence over the placement angle when forming the second mapping of the discrete sample values. 63. The apparatus of claim 54, wherein the fourth mapping has a different resolution than the first mapping. 64. The apparatus according to claim 54, wherein said image data is color image data. 65. Second calculating means for calculating a text index value C, comparing the text index value with a threshold value, and comparing the labeling of each discrete sample value in each text region based on the comparison. The apparatus of claim 54, further comprising: 66. The text index C is: C = max
(| P ₀ −P _i |), i∈1,. . , 8 and i
66. The apparatus of claim 65, wherein is the index of the eight nearest discrete samples closest to the central discrete sample value P0. 67. The apparatus according to claim 65, wherein said means for identifying performs a cleaning operation of said text label. 68. The cleaning operation according to claim 6, wherein the cleaning operation is a morphological opening operation.
An apparatus according to claim 7. 69. A function for calculating an edge response value for each of the discrete sample values, a function for calculating a gradient magnitude value based on the edge response value, and a threshold value for the gradient magnitude value. A function of classifying the current pixel based on the comparison, a function of calculating the arrangement angle for the current pixel based on the comparison, and a function of storing the arrangement angle. 55. The apparatus of claim 54, wherein 70. The gradient magnitude value G _m is G _m = (G _v ² + G _h ² ), where G _v and G _h are the vertical edge response and the horizontal edge response, respectively. Equipment. 71. Assume that G _v and G _h are a vertical edge response and a horizontal edge response, respectively, and
The apparatus of claim 69 which is _{^{Gθ = tan -1 (G v /}} G h). 72. The operating means includes: (i) a function of accumulating a large number of discrete data values at each arrangement angle for one of a plurality of parts of the discrete data values; and (ii) a discrete sample for each arrangement angle. (Iii) comparing the maximum value and the minimum value to a maximum threshold value and a minimum threshold value, respectively; and (iv) the discrete data value of the portion based on the comparison. 55. The method according to claim 54, wherein the function is configured to perform a function of reassigning the arrangement angle of (i) and (v) a function of repeating the functions (i) to (iv) for each of the portions of the discrete data value. apparatus. 73. The apparatus of claim 72, wherein the plurality of portions of the discrete data value are five portions. 74. The apparatus of claim 54, wherein the modified cubic interpolation kernel is applied to discrete data values labeled as text. 75. The modified cubic interpolation kernel h (s), where s = t / Δt is a normalized coordinate having an integer value at a sample point, where 0 ≦ d <0.5.
Is: 75. The device of claim 74 in the form of: 76. The apparatus of claim 74, wherein a steerable cubic interpolation kernel is applied to discrete data values classified as edges. 77. The steerable third order, where s _x = x / Δx and s _y = y / Δy are horizontal and vertical resampling distances respectively, and “·” indicates matrix multiplication. The interpolation kernel is 77. The device of claim 76 in the form: 78. The apparatus of claim 76, wherein a conventional cubic interpolation kernel is applied to discrete data values classified as smooth. 79. Assuming that b = 0 and c = 0.5, the conventional cubic interpolation kernel is given by: 79. The device of claim 78 in the form of: 80. A computer readable medium for storing a program for an apparatus for processing data, wherein the processing includes a method for interpolating image data including a first mapping of discrete sample values. A code for identifying a text region in the first mapping and labeling each discrete sample value in each text region; and calculating edge information for each discrete sample value in the image data. A code for identifying an edge sample value and storing an arrangement angle for each edge sample value; combining the label and the arrangement angle for each discrete sample value to form a second mapping of the discrete sample values. Code for forming; and manipulating the placement angle for each edge sample in the second mapping A code for forming a third mapping of the discrete sample values, a code for manipulating the image data of the third mapping to form a fourth mapping of the image data, Forming a fifth mapping of the image data by interpolating each sample value of the fourth mapping with a first kernel among a plurality of kernels according to the label of the respective sample values of the mapping and the arrangement angle. And a computer readable medium containing code for performing 81. The program further comprises: converting each discrete sample value of the fourth mapping to the third
81. The computer readable code of claim 80, further comprising: code for associating the mapping with a corresponding discrete sample value; and code for scaling the third mapping of the image data based on the association. Medium. 82. The computer-readable medium of claim 80, further comprising code for interpolating the image data of the third mapping using a second kernel. 83. The computer readable medium according to claim 82, wherein said second kernel is an NN interpolation kernel. 84. The method of claim 1, wherein the label of the sample values of the fourth mapping and the placement angle are used.
Selecting a kernel parameter value for the kernel of claim 8.
0. The computer-readable medium according to 0. 85. The computer readable medium according to claim 80, wherein said first kernel is a universal interpolation kernel h (s). 86. Assuming that s = t / Δt and 0 ≦ d <0.5, the general-purpose interpolation kernel h (s) is given by: 86. The computer readable medium of claim 85 in the form of: 87. Assuming that s _x = x / Δx and s _y = y / Δy are horizontal and vertical resampling distances respectively, and “·” indicates a matrix multiplication, the plurality of kernels are (Equation 2) 81. The computer readable medium of claim 80 provided by: 88. The computer readable medium of claim 80, wherein a label takes precedence over said placement angle when forming said second mapping of said discrete sample values. 89. The computer readable medium according to claim 80, wherein the fourth mapping has a different resolution than the first mapping. 90. The computer readable medium according to claim 80, wherein said image data is color image data. 91. The program further comprises: code for calculating a text index value C; comparing the text index value to a threshold; wherein the labeling of each discrete sample value in each text region is based on the comparison. 81. The computer readable medium of claim 80, comprising: code for comparison. 92. The text index C is: C = max
(| P ₀ −P _i |), i∈1,. . , 8 and i
92. The computer-readable medium of claim 91, wherein is the index of the eight nearest discrete samples closest to the central discrete sample value P0. 93. The computer-readable medium according to claim 91, wherein the program further includes code for executing an operation of cleaning the text label. 94. The cleaning operation according to claim 9, wherein the cleaning operation is a morphological opening operation.
4. The computer readable medium according to claim 3. 95. The program further comprises: a code for calculating an edge response value for each of the discrete sample values; a code for calculating a gradient magnitude value based on the edge response value; A code for comparing with a threshold value, a code for classifying a current pixel based on the comparison, a code for calculating the layout angle for the current pixel based on the comparison, and storing the layout angle 9. The code of claim 8,
0. The computer-readable medium according to 0. 96. The gradient magnitude value G _m is G _m = (G _v ² + G _h ² ), where G _v and G _h are the vertical edge response and the horizontal edge response, respectively. Computer readable media. 97. Assuming that G _v and G _h are a vertical edge response and a horizontal edge response, respectively,
_{^{Is, Gθ = tan -1 (G v}} / G h) a The computer program of claim 95 is. 98. The program further comprises: code for accumulating a number of discrete data values for each of the configuration angles for one of the plurality of portions of the discrete data value; and a maximum value of the discrete sample values for each of the configuration angles. And a code for calculating a minimum value, a code for comparing the maximum value and the minimum value with a maximum threshold value and a minimum threshold value, respectively, and reassigning the arrangement angle of the discrete data value of the portion based on the comparison And a code for performing
A computer-readable medium according to claim 1. 99. The computer readable medium of claim 80, wherein the modified cubic interpolation kernel is applied to discrete data values labeled as text. 100. The modulated cubic interpolation kernel h (s), where s = t / Δt is a normalized coordinate having an integer value at a sample point, where 0 ≦ d <0.5.
Is: The computer-readable medium of claim 98, wherein the medium is in the form of: 101. The steerable cubic interpolation kernel applied to discrete data values classified as edges.
A computer-readable medium according to claim 1. 102. Assuming that s _x = x / Δx and s _y = y / Δy are resampling distances in the horizontal direction and the vertical direction, respectively, and The interpolation kernel is 102. The computer readable medium of claim 101 in the form of: 103. A conventional cubic interpolation kernel applied to discrete data values classified as smooth.
A computer-readable medium according to claim 1. 104. Assuming that b = 0 and c = 0.5, the conventional cubic interpolation kernel is given by: 102. The computer readable medium of claim 101 in the form of: 105. A method for interpolating a first set of discrete sample values using one of a plurality of interpolation kernels to generate a second set of discrete sample values, as illustrated in the accompanying drawings. Described as in any of the described embodiments. 106. A method of interpolating image data, substantially as described in any of the embodiments illustrated in the accompanying drawings. 107. An apparatus for interpolating image data, substantially as described in any of the embodiments illustrated in the accompanying drawings. 108. A computer readable medium storing a program for an apparatus for processing data, wherein the processing includes a method of interpolating image data, the program including any of the methods illustrated in the accompanying drawings. A computer-readable medium substantially as described in any of the embodiments.